Now let us suppose that \((M^n,g)\)  is a SKL manifold. By [1]}, we know that \(g\)  is pluriclosed, and \(\nabla ^sT^s=0\) . Clearly, the latter is equivalent to \(\nabla ^sT=0\) . Thus by (REF ), we know that for any SKL manifold, the Chern covariant derivative of the torsion is given by a quadratic form of the torsion:
\(T^j_{ik, \overline{\ell }} = \sum _r \big ( - T^j_{kr} \overline{ T^i_{\ell r}} + T^j_{ir} \overline{ T^k_{\ell r}} + T^r_{ik} \overline{ T^r_{j\ell }} \big ) \) 
